Triangle Sum Conjecture

Explanation:

Many students may already be familiar with this conjecture, which states that the angles in a triangle add up to 180 degrees. Stating the conjecture is fairly easy, and demonstrating it can be fun. We have included some nice classroom demonstrations in the Activity Sheet for this conjecture. I encourage you to try them out!

The power of the Triangle Sum Conjecture cannot be understated. Many of the upcoming problem solving activities and proofs of conjectures will require a very good understanding of how it can be used. Let us demonstrate a typical example:

Sample Problem:

Problem: Suppose that we are given triangle ABC such that:

Angle A = 40 degrees

Angle B = 80 degrees

Can we find angle C?

Solution: We know that the sum of the angles must be 180 degrees. Since angles A and B already add up to 120 degrees, this leaves 60 degrees for angle C. Using algebra, this can be represented by:

A + B + C = 180
40 + 80 + C = 180
120 + C = 180C = 60

So this conjecture tells us that if we know two of the angles in a triangle, then we can find the third angle quite simply.

The precise statement of the conjecture is:

Conjecture (Triangle Sum ):
The sum of the interior angles in any triangle is 180 degrees.